Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Smythe, Iian B."'
For each $n\geq 2$, we show that the class of all finite $n$-dimensional partial orders, when expanded with $n$ linear orders which realize the partial order, forms a Fra\"iss\'e class and identify its Fra\"iss\'e limit $(D_n,<,<_1,\ldots,<_n)$. We g
Externí odkaz:
http://arxiv.org/abs/2412.18704
Autor:
Smythe, Iian B.
We show that the Ramsey theory of block sequences in infinite-dimensional discrete vector spaces can be parametrized by perfect sets. As special cases, we prove combinatorial dichotomies for definable families of partitions and linear transformations
Externí odkaz:
http://arxiv.org/abs/2108.00544
Autor:
Smythe, Iian B.
Publikováno v:
Fund. Math. 260 (2023), 41-58
We study various combinatorial properties, and the implications between them, for filters generated by infinite-dimensional subspaces of a countable vector space. These properties are analogous to selectivity for ultrafilters on the natural numbers a
Externí odkaz:
http://arxiv.org/abs/2101.06501
Autor:
Smythe, Iian B.
Publikováno v:
Colloq. Math. 163 (2021), 15-22
We show that a parametrized $\diamondsuit$ principle, corresponding to the uniformity of the meager ideal, implies that the minimum cardinality of an infinite maximal almost disjoint family of block subspaces in a countable vector space is $\aleph_1$
Externí odkaz:
http://arxiv.org/abs/1909.08078
Autor:
Smythe, Iian B.
Publikováno v:
Arch. Math. Log. 61 (2022), 795-812
Given a countable transitive model of set theory and a partial order contained in it, there is a natural countable Borel equivalence relation on generic filters over the model; two are equivalent if they yield the same generic extension. We examine t
Externí odkaz:
http://arxiv.org/abs/1810.04704
Autor:
Smythe, Iian B.
Publikováno v:
J. symb. log. 84 (2019) 1590-1611
We consider maximal almost disjoint families of block subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite cardinality of such a family cannot be decided in ZFC and that the "s
Externí odkaz:
http://arxiv.org/abs/1712.00057
Autor:
Smythe, Iian B.
Publikováno v:
Trans. Amer. Math. Soc. 370 (2018), 8859-8893
We develop local forms of Ramsey-theoretic dichotomies for block sequences in infinite-dimensional vector spaces, analogous to Mathias' selective coideal form of Silver's theorem for analytic partitions of $[\mathbb{N}]^\infty$. Under large cardinals
Externí odkaz:
http://arxiv.org/abs/1609.09016
Autor:
Smythe, Iian B.
Publikováno v:
Fund. Math. 237 (2017), no. 1, 31-45
We consider various notions of equivalence in the space of bounded operators on a Hilbert space, in particular modulo finite rank, modulo Schatten $p$-class, and modulo compact. Using Hjorth's theory of turbulence, the latter two are shown to be not
Externí odkaz:
http://arxiv.org/abs/1407.5325
Autor:
SMYTHE, IIAN B.
Publikováno v:
The Journal of Symbolic Logic, 2019 Dec 01. 84(4), 1590-1611.
Externí odkaz:
https://www.jstor.org/stable/26873317
Autor:
Smythe, Iian B.
It is well known that every locally compact abelian group L can be decomposed as L_1 \oplus R^n, where L_1 contains a compact-open subgroup. In this paper, we use this decomposition to study the topological group Aut(L) of automorphisms of L, equippe
Externí odkaz:
http://arxiv.org/abs/1110.1923